Question

Which function does not have a vertical asymptote? A) y=(x) /(1+x²) . B) y=(5x) /(1-x²) . C) y=(5x-1) /(x) . D) (5x) /(x+x²) .

Answer 1

V A are vertical lines that correspond to zeroes of the denominator of a rational function.
B ) Denominator: 1 - x² = 0
x² = 1,  x = 1, or x = - 1
C ) x = 0
D ) x + x² = 0
x ( 1 + x ) = 0,  x = 0 or x = - 1
And finally:
A ) 1 + x² ≠ 0,  x² ≠ - 1
Answer: function A ) does not have a vertical asymptote.